Change the angle pivot of my object
Let's you have this setup here, similar to yours:

 
Cylinder fits 2 cubes, but it's orientation is broken. And you want to fix it.
Create a Custom Transform Orientation. For this simple example: select the edge you want to align, press CtrlAltSpace or find it at bottom of the N-Panel.

You will have a new transform orientation that fits to geometry:


Now you can use this transform orientation for scale your object. But If you want to align object itself, move next.
In object Mode select cylinder, and press ShiftS -> Cursor to Selected
Create empty then press Object -> Transform -> Align to transform Orientation.
Parent cylinder to the empty  CtrlP.
Clear empty's orientation AltR. Cylinder will follow empty and will rotate with it like this:


Unparent cylinder AltP -> Clear and keep transform.
Apply rotation to cylinder  AltA -> Rotation
Rotate cylinder back ( Object -> Transform -> Align to transform Orientation. )